Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [483,2,Mod(160,483)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(483, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("483.160");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 483 = 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 483.h (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.85677441763\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 17x^{10} + 92x^{8} + 180x^{6} + 92x^{4} + 17x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 160.2 | ||
Root | \(-2.92914i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 483.160 |
Dual form | 483.2.h.c.160.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/483\mathbb{Z}\right)^\times\).
\(n\) | \(323\) | \(346\) | \(442\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.69639 | −1.90664 | −0.953319 | − | 0.301966i | \(-0.902357\pi\) | ||||
−0.953319 | + | 0.301966i | \(0.902357\pi\) | |||||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | 5.27053 | 2.63527 | ||||||||
\(5\) | 2.58774 | 1.15727 | 0.578636 | − | 0.815586i | \(-0.303585\pi\) | ||||
0.578636 | + | 0.815586i | \(0.303585\pi\) | |||||||
\(6\) | 2.69639i | 1.10080i | ||||||||
\(7\) | 0.551006 | − | 2.58774i | 0.208261 | − | 0.978073i | ||||
\(8\) | −8.81864 | −3.11786 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | −6.97756 | −2.20650 | ||||||||
\(11\) | − | 3.13874i | − | 0.946367i | −0.880964 | − | 0.473184i | \(-0.843105\pi\) | ||
0.880964 | − | 0.473184i | \(-0.156895\pi\) | |||||||
\(12\) | − | 5.27053i | − | 1.52147i | ||||||
\(13\) | − | 4.69639i | − | 1.30254i | −0.758844 | − | 0.651272i | \(-0.774235\pi\) | ||
0.758844 | − | 0.651272i | \(-0.225765\pi\) | |||||||
\(14\) | −1.48573 | + | 6.97756i | −0.397077 | + | 1.86483i | ||||
\(15\) | − | 2.58774i | − | 0.668151i | ||||||
\(16\) | 13.2375 | 3.30937 | ||||||||
\(17\) | −6.97756 | −1.69231 | −0.846154 | − | 0.532939i | \(-0.821087\pi\) | ||||
−0.846154 | + | 0.532939i | \(0.821087\pi\) | |||||||
\(18\) | 2.69639 | 0.635546 | ||||||||
\(19\) | 3.13874 | 0.720077 | 0.360039 | − | 0.932937i | \(-0.382763\pi\) | ||||
0.360039 | + | 0.932937i | \(0.382763\pi\) | |||||||
\(20\) | 13.6388 | 3.04972 | ||||||||
\(21\) | −2.58774 | − | 0.551006i | −0.564691 | − | 0.120239i | ||||
\(22\) | 8.46329i | 1.80438i | ||||||||
\(23\) | −1.27053 | + | 4.62447i | −0.264925 | + | 0.964269i | ||||
\(24\) | 8.81864i | 1.80010i | ||||||||
\(25\) | 1.69639 | 0.339279 | ||||||||
\(26\) | 12.6633i | 2.48348i | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 2.90409 | − | 13.6388i | 0.548822 | − | 2.57748i | ||||
\(29\) | 3.96693 | 0.736640 | 0.368320 | − | 0.929699i | \(-0.379933\pi\) | ||||
0.368320 | + | 0.929699i | \(0.379933\pi\) | |||||||
\(30\) | 6.97756i | 1.27392i | ||||||||
\(31\) | 2.57414i | 0.462329i | 0.972915 | + | 0.231165i | \(0.0742536\pi\) | ||||
−0.972915 | + | 0.231165i | \(0.925746\pi\) | |||||||
\(32\) | −18.0561 | −3.19190 | ||||||||
\(33\) | −3.13874 | −0.546385 | ||||||||
\(34\) | 18.8142 | 3.22662 | ||||||||
\(35\) | 1.42586 | − | 6.69639i | 0.241014 | − | 1.13190i | ||||
\(36\) | −5.27053 | −0.878422 | ||||||||
\(37\) | 2.90409i | 0.477430i | 0.971090 | + | 0.238715i | \(0.0767262\pi\) | ||||
−0.971090 | + | 0.238715i | \(0.923274\pi\) | |||||||
\(38\) | −8.46329 | −1.37293 | ||||||||
\(39\) | −4.69639 | −0.752025 | ||||||||
\(40\) | −22.8203 | −3.60821 | ||||||||
\(41\) | − | 5.00000i | − | 0.780869i | −0.920631 | − | 0.390434i | \(-0.872325\pi\) | ||
0.920631 | − | 0.390434i | \(-0.127675\pi\) | |||||||
\(42\) | 6.97756 | + | 1.48573i | 1.07666 | + | 0.229253i | ||||
\(43\) | 0.785656i | 0.119811i | 0.998204 | + | 0.0599057i | \(0.0190800\pi\) | ||||
−0.998204 | + | 0.0599057i | \(0.980920\pi\) | |||||||
\(44\) | − | 16.5429i | − | 2.49393i | ||||||
\(45\) | −2.58774 | −0.385757 | ||||||||
\(46\) | 3.42586 | − | 12.4694i | 0.505115 | − | 1.83851i | ||||
\(47\) | − | 12.3597i | − | 1.80285i | −0.432936 | − | 0.901425i | \(-0.642522\pi\) | ||
0.432936 | − | 0.901425i | \(-0.357478\pi\) | |||||||
\(48\) | − | 13.2375i | − | 1.91066i | ||||||
\(49\) | −6.39279 | − | 2.85172i | −0.913255 | − | 0.407388i | ||||
\(50\) | −4.57414 | −0.646881 | ||||||||
\(51\) | 6.97756i | 0.977054i | ||||||||
\(52\) | − | 24.7525i | − | 3.43255i | ||||||
\(53\) | 7.52857i | 1.03413i | 0.855947 | + | 0.517064i | \(0.172975\pi\) | ||||
−0.855947 | + | 0.517064i | \(0.827025\pi\) | |||||||
\(54\) | − | 2.69639i | − | 0.366933i | ||||||
\(55\) | − | 8.12225i | − | 1.09520i | ||||||
\(56\) | −4.85912 | + | 22.8203i | −0.649328 | + | 3.04950i | ||||
\(57\) | − | 3.13874i | − | 0.415737i | ||||||
\(58\) | −10.6964 | −1.40451 | ||||||||
\(59\) | 3.15532i | 0.410788i | 0.978679 | + | 0.205394i | \(0.0658476\pi\) | ||||
−0.978679 | + | 0.205394i | \(0.934152\pi\) | |||||||
\(60\) | − | 13.6388i | − | 1.76076i | ||||||
\(61\) | −8.22864 | −1.05357 | −0.526785 | − | 0.849999i | \(-0.676603\pi\) | ||||
−0.526785 | + | 0.849999i | \(0.676603\pi\) | |||||||
\(62\) | − | 6.94090i | − | 0.881495i | ||||||
\(63\) | −0.551006 | + | 2.58774i | −0.0694202 | + | 0.326024i | ||||
\(64\) | 22.2114 | 2.77643 | ||||||||
\(65\) | − | 12.1530i | − | 1.50740i | ||||||
\(66\) | 8.46329 | 1.04176 | ||||||||
\(67\) | 7.76322i | 0.948428i | 0.880410 | + | 0.474214i | \(0.157268\pi\) | ||||
−0.880410 | + | 0.474214i | \(0.842732\pi\) | |||||||
\(68\) | −36.7755 | −4.45968 | ||||||||
\(69\) | 4.62447 | + | 1.27053i | 0.556721 | + | 0.152954i | ||||
\(70\) | −3.84468 | + | 18.0561i | −0.459527 | + | 2.15812i | ||||
\(71\) | 9.23746 | 1.09628 | 0.548142 | − | 0.836385i | \(-0.315335\pi\) | ||||
0.548142 | + | 0.836385i | \(0.315335\pi\) | |||||||
\(72\) | 8.81864 | 1.03929 | ||||||||
\(73\) | − | 9.65628i | − | 1.13018i | −0.825029 | − | 0.565091i | \(-0.808841\pi\) | ||
0.825029 | − | 0.565091i | \(-0.191159\pi\) | |||||||
\(74\) | − | 7.83058i | − | 0.910286i | ||||||
\(75\) | − | 1.69639i | − | 0.195883i | ||||||
\(76\) | 16.5429 | 1.89760 | ||||||||
\(77\) | −8.12225 | − | 1.72947i | −0.925616 | − | 0.197091i | ||||
\(78\) | 12.6633 | 1.43384 | ||||||||
\(79\) | 1.50395i | 0.169208i | 0.996415 | + | 0.0846039i | \(0.0269625\pi\) | ||||
−0.996415 | + | 0.0846039i | \(0.973038\pi\) | |||||||
\(80\) | 34.2551 | 3.82984 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 13.4820i | 1.48883i | ||||||||
\(83\) | 15.7572 | 1.72958 | 0.864789 | − | 0.502136i | \(-0.167452\pi\) | ||||
0.864789 | + | 0.502136i | \(0.167452\pi\) | |||||||
\(84\) | −13.6388 | − | 2.90409i | −1.48811 | − | 0.316863i | ||||
\(85\) | −18.0561 | −1.95846 | ||||||||
\(86\) | − | 2.11844i | − | 0.228437i | ||||||
\(87\) | − | 3.96693i | − | 0.425299i | ||||||
\(88\) | 27.6795i | 2.95064i | ||||||||
\(89\) | 2.18580 | 0.231694 | 0.115847 | − | 0.993267i | \(-0.463042\pi\) | ||||
0.115847 | + | 0.993267i | \(0.463042\pi\) | |||||||
\(90\) | 6.97756 | 0.735499 | ||||||||
\(91\) | −12.1530 | − | 2.58774i | −1.27398 | − | 0.271269i | ||||
\(92\) | −6.69639 | + | 24.3734i | −0.698147 | + | 2.54111i | ||||
\(93\) | 2.57414 | 0.266926 | ||||||||
\(94\) | 33.3266i | 3.43738i | ||||||||
\(95\) | 8.12225 | 0.833325 | ||||||||
\(96\) | 18.0561i | 1.84284i | ||||||||
\(97\) | −7.74499 | −0.786385 | −0.393192 | − | 0.919456i | \(-0.628629\pi\) | ||||
−0.393192 | + | 0.919456i | \(0.628629\pi\) | |||||||
\(98\) | 17.2375 | + | 7.68935i | 1.74125 | + | 0.776742i | ||||
\(99\) | 3.13874i | 0.315456i | ||||||||
\(100\) | 8.94090 | 0.894090 | ||||||||
\(101\) | − | 7.38574i | − | 0.734909i | −0.930042 | − | 0.367454i | \(-0.880229\pi\) | ||
0.930042 | − | 0.367454i | \(-0.119771\pi\) | |||||||
\(102\) | − | 18.8142i | − | 1.86289i | ||||||
\(103\) | 5.41013 | 0.533076 | 0.266538 | − | 0.963824i | \(-0.414120\pi\) | ||||
0.266538 | + | 0.963824i | \(0.414120\pi\) | |||||||
\(104\) | 41.4158i | 4.06116i | ||||||||
\(105\) | −6.69639 | − | 1.42586i | −0.653501 | − | 0.139150i | ||||
\(106\) | − | 20.3000i | − | 1.97171i | ||||||
\(107\) | − | 2.98968i | − | 0.289023i | −0.989503 | − | 0.144512i | \(-0.953839\pi\) | ||
0.989503 | − | 0.144512i | \(-0.0461611\pi\) | |||||||
\(108\) | 5.27053i | 0.507157i | ||||||||
\(109\) | 4.45718i | 0.426921i | 0.976952 | + | 0.213460i | \(0.0684734\pi\) | ||||
−0.976952 | + | 0.213460i | \(0.931527\pi\) | |||||||
\(110\) | 21.9008i | 2.08816i | ||||||||
\(111\) | 2.90409 | 0.275644 | ||||||||
\(112\) | 7.29392 | − | 34.2551i | 0.689210 | − | 3.23680i | ||||
\(113\) | − | 20.6163i | − | 1.93942i | −0.244257 | − | 0.969710i | \(-0.578544\pi\) | ||
0.244257 | − | 0.969710i | \(-0.421456\pi\) | |||||||
\(114\) | 8.46329i | 0.792660i | ||||||||
\(115\) | −3.28781 | + | 11.9669i | −0.306590 | + | 1.11592i | ||||
\(116\) | 20.9078 | 1.94124 | ||||||||
\(117\) | 4.69639i | 0.434182i | ||||||||
\(118\) | − | 8.50799i | − | 0.783224i | ||||||
\(119\) | −3.84468 | + | 18.0561i | −0.352441 | + | 1.65520i | ||||
\(120\) | 22.8203i | 2.08320i | ||||||||
\(121\) | 1.14828 | 0.104389 | ||||||||
\(122\) | 22.1876 | 2.00877 | ||||||||
\(123\) | −5.00000 | −0.450835 | ||||||||
\(124\) | 13.5671i | 1.21836i | ||||||||
\(125\) | −8.54887 | −0.764634 | ||||||||
\(126\) | 1.48573 | − | 6.97756i | 0.132359 | − | 0.621611i | ||||
\(127\) | 19.0561 | 1.69096 | 0.845478 | − | 0.534010i | \(-0.179316\pi\) | ||||
0.845478 | + | 0.534010i | \(0.179316\pi\) | |||||||
\(128\) | −23.7785 | −2.10174 | ||||||||
\(129\) | 0.785656 | 0.0691732 | ||||||||
\(130\) | 32.7694i | 2.87406i | ||||||||
\(131\) | − | 10.1483i | − | 0.886660i | −0.896359 | − | 0.443330i | \(-0.853797\pi\) | ||
0.896359 | − | 0.443330i | \(-0.146203\pi\) | |||||||
\(132\) | −16.5429 | −1.43987 | ||||||||
\(133\) | 1.72947 | − | 8.12225i | 0.149964 | − | 0.704289i | ||||
\(134\) | − | 20.9327i | − | 1.80831i | ||||||
\(135\) | 2.58774i | 0.222717i | ||||||||
\(136\) | 61.5326 | 5.27638 | ||||||||
\(137\) | − | 4.71006i | − | 0.402407i | −0.979549 | − | 0.201204i | \(-0.935515\pi\) | ||
0.979549 | − | 0.201204i | \(-0.0644853\pi\) | |||||||
\(138\) | −12.4694 | − | 3.42586i | −1.06147 | − | 0.291628i | ||||
\(139\) | − | 2.43290i | − | 0.206356i | −0.994663 | − | 0.103178i | \(-0.967099\pi\) | ||
0.994663 | − | 0.103178i | \(-0.0329011\pi\) | |||||||
\(140\) | 7.51504 | − | 35.2936i | 0.635137 | − | 2.98285i | ||||
\(141\) | −12.3597 | −1.04088 | ||||||||
\(142\) | −24.9078 | −2.09022 | ||||||||
\(143\) | −14.7408 | −1.23269 | ||||||||
\(144\) | −13.2375 | −1.10312 | ||||||||
\(145\) | 10.2654 | 0.852493 | ||||||||
\(146\) | 26.0371i | 2.15485i | ||||||||
\(147\) | −2.85172 | + | 6.39279i | −0.235206 | + | 0.527268i | ||||
\(148\) | 15.3061i | 1.25816i | ||||||||
\(149\) | 19.6634i | 1.61089i | 0.592673 | + | 0.805443i | \(0.298073\pi\) | ||||
−0.592673 | + | 0.805443i | \(0.701927\pi\) | |||||||
\(150\) | 4.57414i | 0.373477i | ||||||||
\(151\) | 4.72242 | 0.384305 | 0.192153 | − | 0.981365i | \(-0.438453\pi\) | ||||
0.192153 | + | 0.981365i | \(0.438453\pi\) | |||||||
\(152\) | −27.6795 | −2.24510 | ||||||||
\(153\) | 6.97756 | 0.564102 | ||||||||
\(154\) | 21.9008 | + | 4.66332i | 1.76482 | + | 0.375781i | ||||
\(155\) | 6.66121i | 0.535041i | ||||||||
\(156\) | −24.7525 | −1.98179 | ||||||||
\(157\) | 9.48360 | 0.756873 | 0.378437 | − | 0.925627i | \(-0.376462\pi\) | ||||
0.378437 | + | 0.925627i | \(0.376462\pi\) | |||||||
\(158\) | − | 4.05524i | − | 0.322618i | ||||||
\(159\) | 7.52857 | 0.597054 | ||||||||
\(160\) | −46.7245 | −3.69389 | ||||||||
\(161\) | 11.2669 | + | 5.83592i | 0.887953 | + | 0.459935i | ||||
\(162\) | −2.69639 | −0.211849 | ||||||||
\(163\) | −6.54811 | −0.512888 | −0.256444 | − | 0.966559i | \(-0.582551\pi\) | ||||
−0.256444 | + | 0.966559i | \(0.582551\pi\) | |||||||
\(164\) | − | 26.3527i | − | 2.05780i | ||||||
\(165\) | −8.12225 | −0.632316 | ||||||||
\(166\) | −42.4876 | −3.29768 | ||||||||
\(167\) | 22.0301i | 1.70474i | 0.522941 | + | 0.852369i | \(0.324835\pi\) | ||||
−0.522941 | + | 0.852369i | \(0.675165\pi\) | |||||||
\(168\) | 22.8203 | + | 4.85912i | 1.76063 | + | 0.374889i | ||||
\(169\) | −9.05611 | −0.696623 | ||||||||
\(170\) | 48.6864 | 3.73407 | ||||||||
\(171\) | −3.13874 | −0.240026 | ||||||||
\(172\) | 4.14083i | 0.315735i | ||||||||
\(173\) | − | 19.6563i | − | 1.49444i | −0.664577 | − | 0.747220i | \(-0.731388\pi\) | ||
0.664577 | − | 0.747220i | \(-0.268612\pi\) | |||||||
\(174\) | 10.6964i | 0.810891i | ||||||||
\(175\) | 0.934722 | − | 4.38982i | 0.0706583 | − | 0.331839i | ||||
\(176\) | − | 41.5490i | − | 3.13187i | ||||||
\(177\) | 3.15532 | 0.237169 | ||||||||
\(178\) | −5.89377 | −0.441757 | ||||||||
\(179\) | 9.51504 | 0.711187 | 0.355594 | − | 0.934641i | \(-0.384279\pi\) | ||||
0.355594 | + | 0.934641i | \(0.384279\pi\) | |||||||
\(180\) | −13.6388 | −1.01657 | ||||||||
\(181\) | 10.5817 | 0.786533 | 0.393267 | − | 0.919424i | \(-0.371345\pi\) | ||||
0.393267 | + | 0.919424i | \(0.371345\pi\) | |||||||
\(182\) | 32.7694 | + | 6.97756i | 2.42903 | + | 0.517211i | ||||
\(183\) | 8.22864i | 0.608278i | ||||||||
\(184\) | 11.2044 | − | 40.7816i | 0.825998 | − | 3.00646i | ||||
\(185\) | 7.51504i | 0.552517i | ||||||||
\(186\) | −6.94090 | −0.508931 | ||||||||
\(187\) | 21.9008i | 1.60154i | ||||||||
\(188\) | − | 65.1423i | − | 4.75099i | ||||||
\(189\) | 2.58774 | + | 0.551006i | 0.188230 | + | 0.0400798i | ||||
\(190\) | −21.9008 | −1.58885 | ||||||||
\(191\) | − | 11.9857i | − | 0.867258i | −0.901091 | − | 0.433629i | \(-0.857233\pi\) | ||
0.901091 | − | 0.433629i | \(-0.142767\pi\) | |||||||
\(192\) | − | 22.2114i | − | 1.60297i | ||||||
\(193\) | 2.96693 | 0.213564 | 0.106782 | − | 0.994282i | \(-0.465945\pi\) | ||||
0.106782 | + | 0.994282i | \(0.465945\pi\) | |||||||
\(194\) | 20.8835 | 1.49935 | ||||||||
\(195\) | −12.1530 | −0.870297 | ||||||||
\(196\) | −33.6934 | − | 15.0301i | −2.40667 | − | 1.07358i | ||||
\(197\) | 16.9268 | 1.20599 | 0.602993 | − | 0.797747i | \(-0.293975\pi\) | ||||
0.602993 | + | 0.797747i | \(0.293975\pi\) | |||||||
\(198\) | − | 8.46329i | − | 0.601460i | ||||||
\(199\) | −15.2062 | −1.07794 | −0.538969 | − | 0.842325i | \(-0.681186\pi\) | ||||
−0.538969 | + | 0.842325i | \(0.681186\pi\) | |||||||
\(200\) | −14.9599 | −1.05782 | ||||||||
\(201\) | 7.76322 | 0.547575 | ||||||||
\(202\) | 19.9149i | 1.40121i | ||||||||
\(203\) | 2.18580 | − | 10.2654i | 0.153413 | − | 0.720488i | ||||
\(204\) | 36.7755i | 2.57480i | ||||||||
\(205\) | − | 12.9387i | − | 0.903678i | ||||||
\(206\) | −14.5878 | −1.01638 | ||||||||
\(207\) | 1.27053 | − | 4.62447i | 0.0883082 | − | 0.321423i | ||||
\(208\) | − | 62.1683i | − | 4.31060i | ||||||
\(209\) | − | 9.85172i | − | 0.681458i | ||||||
\(210\) | 18.0561 | + | 3.84468i | 1.24599 | + | 0.265308i | ||||
\(211\) | 18.3928 | 1.26621 | 0.633106 | − | 0.774065i | \(-0.281780\pi\) | ||||
0.633106 | + | 0.774065i | \(0.281780\pi\) | |||||||
\(212\) | 39.6796i | 2.72520i | ||||||||
\(213\) | − | 9.23746i | − | 0.632940i | ||||||
\(214\) | 8.06135i | 0.551062i | ||||||||
\(215\) | 2.03307i | 0.138654i | ||||||||
\(216\) | − | 8.81864i | − | 0.600033i | ||||||
\(217\) | 6.66121 | + | 1.41837i | 0.452192 | + | 0.0962850i | ||||
\(218\) | − | 12.0183i | − | 0.813983i | ||||||
\(219\) | −9.65628 | −0.652511 | ||||||||
\(220\) | − | 42.8086i | − | 2.88616i | ||||||
\(221\) | 32.7694i | 2.20431i | ||||||||
\(222\) | −7.83058 | −0.525554 | ||||||||
\(223\) | 3.02603i | 0.202638i | 0.994854 | + | 0.101319i | \(0.0323063\pi\) | ||||
−0.994854 | + | 0.101319i | \(0.967694\pi\) | |||||||
\(224\) | −9.94902 | + | 46.7245i | −0.664747 | + | 3.12191i | ||||
\(225\) | −1.69639 | −0.113093 | ||||||||
\(226\) | 55.5897i | 3.69777i | ||||||||
\(227\) | 8.53065 | 0.566199 | 0.283100 | − | 0.959091i | \(-0.408637\pi\) | ||||
0.283100 | + | 0.959091i | \(0.408637\pi\) | |||||||
\(228\) | − | 16.5429i | − | 1.09558i | ||||||
\(229\) | 10.8346 | 0.715971 | 0.357985 | − | 0.933727i | \(-0.383464\pi\) | ||||
0.357985 | + | 0.933727i | \(0.383464\pi\) | |||||||
\(230\) | 8.86523 | − | 32.2675i | 0.584556 | − | 2.12766i | ||||
\(231\) | −1.72947 | + | 8.12225i | −0.113791 | + | 0.534405i | ||||
\(232\) | −34.9829 | −2.29674 | ||||||||
\(233\) | −9.27053 | −0.607333 | −0.303666 | − | 0.952778i | \(-0.598211\pi\) | ||||
−0.303666 | + | 0.952778i | \(0.598211\pi\) | |||||||
\(234\) | − | 12.6633i | − | 0.827827i | ||||||
\(235\) | − | 31.9837i | − | 2.08639i | ||||||
\(236\) | 16.6302i | 1.08254i | ||||||||
\(237\) | 1.50395 | 0.0976921 | ||||||||
\(238\) | 10.3668 | − | 48.6864i | 0.671977 | − | 3.15587i | ||||
\(239\) | −11.8777 | −0.768308 | −0.384154 | − | 0.923269i | \(-0.625507\pi\) | ||||
−0.384154 | + | 0.923269i | \(0.625507\pi\) | |||||||
\(240\) | − | 34.2551i | − | 2.21116i | ||||||
\(241\) | −18.4940 | −1.19130 | −0.595652 | − | 0.803243i | \(-0.703106\pi\) | ||||
−0.595652 | + | 0.803243i | \(0.703106\pi\) | |||||||
\(242\) | −3.09622 | −0.199033 | ||||||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | −43.3693 | −2.77644 | ||||||||
\(245\) | −16.5429 | − | 7.37950i | −1.05688 | − | 0.471459i | ||||
\(246\) | 13.4820 | 0.859579 | ||||||||
\(247\) | − | 14.7408i | − | 0.937933i | ||||||
\(248\) | − | 22.7004i | − | 1.44148i | ||||||
\(249\) | − | 15.7572i | − | 0.998572i | ||||||
\(250\) | 23.0511 | 1.45788 | ||||||||
\(251\) | 21.3346 | 1.34663 | 0.673315 | − | 0.739356i | \(-0.264870\pi\) | ||||
0.673315 | + | 0.739356i | \(0.264870\pi\) | |||||||
\(252\) | −2.90409 | + | 13.6388i | −0.182941 | + | 0.859162i | ||||
\(253\) | 14.5150 | + | 3.98788i | 0.912553 | + | 0.250716i | ||||
\(254\) | −51.3827 | −3.22404 | ||||||||
\(255\) | 18.0561i | 1.13072i | ||||||||
\(256\) | 19.6934 | 1.23084 | ||||||||
\(257\) | 15.1973i | 0.947984i | 0.880529 | + | 0.473992i | \(0.157188\pi\) | ||||
−0.880529 | + | 0.473992i | \(0.842812\pi\) | |||||||
\(258\) | −2.11844 | −0.131888 | ||||||||
\(259\) | 7.51504 | + | 1.60017i | 0.466962 | + | 0.0994299i | ||||
\(260\) | − | 64.0530i | − | 3.97240i | ||||||
\(261\) | −3.96693 | −0.245547 | ||||||||
\(262\) | 27.3638i | 1.69054i | ||||||||
\(263\) | 15.2244i | 0.938778i | 0.882991 | + | 0.469389i | \(0.155526\pi\) | ||||
−0.882991 | + | 0.469389i | \(0.844474\pi\) | |||||||
\(264\) | 27.6795 | 1.70355 | ||||||||
\(265\) | 19.4820i | 1.19677i | ||||||||
\(266\) | −4.66332 | + | 21.9008i | −0.285926 | + | 1.34282i | ||||
\(267\) | − | 2.18580i | − | 0.133769i | ||||||
\(268\) | 40.9163i | 2.49936i | ||||||||
\(269\) | 19.5481i | 1.19187i | 0.803033 | + | 0.595935i | \(0.203218\pi\) | ||||
−0.803033 | + | 0.595935i | \(0.796782\pi\) | |||||||
\(270\) | − | 6.97756i | − | 0.424641i | ||||||
\(271\) | 9.11521i | 0.553710i | 0.960912 | + | 0.276855i | \(0.0892921\pi\) | ||||
−0.960912 | + | 0.276855i | \(0.910708\pi\) | |||||||
\(272\) | −92.3652 | −5.60046 | ||||||||
\(273\) | −2.58774 | + | 12.1530i | −0.156617 | + | 0.735535i | ||||
\(274\) | 12.7002i | 0.767245i | ||||||||
\(275\) | − | 5.32454i | − | 0.321082i | ||||||
\(276\) | 24.3734 | + | 6.69639i | 1.46711 | + | 0.403075i | ||||
\(277\) | −21.0702 | −1.26599 | −0.632993 | − | 0.774158i | \(-0.718174\pi\) | ||||
−0.632993 | + | 0.774158i | \(0.718174\pi\) | |||||||
\(278\) | 6.56006i | 0.393446i | ||||||||
\(279\) | − | 2.57414i | − | 0.154110i | ||||||
\(280\) | −12.5741 | + | 59.0531i | −0.751449 | + | 3.52910i | ||||
\(281\) | 13.3224i | 0.794748i | 0.917657 | + | 0.397374i | \(0.130078\pi\) | ||||
−0.917657 | + | 0.397374i | \(0.869922\pi\) | |||||||
\(282\) | 33.3266 | 1.98457 | ||||||||
\(283\) | 1.01643 | 0.0604203 | 0.0302101 | − | 0.999544i | \(-0.490382\pi\) | ||||
0.0302101 | + | 0.999544i | \(0.490382\pi\) | |||||||
\(284\) | 48.6864 | 2.88900 | ||||||||
\(285\) | − | 8.12225i | − | 0.481121i | ||||||
\(286\) | 39.7469 | 2.35028 | ||||||||
\(287\) | −12.9387 | − | 2.75503i | −0.763747 | − | 0.162624i | ||||
\(288\) | 18.0561 | 1.06397 | ||||||||
\(289\) | 31.6864 | 1.86390 | ||||||||
\(290\) | −27.6795 | −1.62539 | ||||||||
\(291\) | 7.74499i | 0.454020i | ||||||||
\(292\) | − | 50.8937i | − | 2.97833i | ||||||
\(293\) | −7.34305 | −0.428986 | −0.214493 | − | 0.976726i | \(-0.568810\pi\) | ||||
−0.214493 | + | 0.976726i | \(0.568810\pi\) | |||||||
\(294\) | 7.68935 | − | 17.2375i | 0.448452 | − | 1.00531i | ||||
\(295\) | 8.16516i | 0.475394i | ||||||||
\(296\) | − | 25.6102i | − | 1.48856i | ||||||
\(297\) | 3.13874 | 0.182128 | ||||||||
\(298\) | − | 53.0202i | − | 3.07138i | ||||||
\(299\) | 21.7183 | + | 5.96693i | 1.25600 | + | 0.345076i | ||||
\(300\) | − | 8.94090i | − | 0.516203i | ||||||
\(301\) | 2.03307 | + | 0.432901i | 0.117184 | + | 0.0249520i | ||||
\(302\) | −12.7335 | −0.732731 | ||||||||
\(303\) | −7.38574 | −0.424300 | ||||||||
\(304\) | 41.5490 | 2.38300 | ||||||||
\(305\) | −21.2936 | −1.21927 | ||||||||
\(306\) | −18.8142 | −1.07554 | ||||||||
\(307\) | 9.98101i | 0.569646i | 0.958580 | + | 0.284823i | \(0.0919349\pi\) | ||||
−0.958580 | + | 0.284823i | \(0.908065\pi\) | |||||||
\(308\) | −42.8086 | − | 9.11521i | −2.43925 | − | 0.519387i | ||||
\(309\) | − | 5.41013i | − | 0.307771i | ||||||
\(310\) | − | 17.9612i | − | 1.02013i | ||||||
\(311\) | 9.95988i | 0.564773i | 0.959301 | + | 0.282387i | \(0.0911261\pi\) | ||||
−0.959301 | + | 0.282387i | \(0.908874\pi\) | |||||||
\(312\) | 41.4158 | 2.34471 | ||||||||
\(313\) | 19.6634 | 1.11144 | 0.555720 | − | 0.831370i | \(-0.312443\pi\) | ||||
0.555720 | + | 0.831370i | \(0.312443\pi\) | |||||||
\(314\) | −25.5715 | −1.44308 | ||||||||
\(315\) | −1.42586 | + | 6.69639i | −0.0803380 | + | 0.377299i | ||||
\(316\) | 7.92663i | 0.445908i | ||||||||
\(317\) | 26.0420 | 1.46267 | 0.731333 | − | 0.682021i | \(-0.238899\pi\) | ||||
0.731333 | + | 0.682021i | \(0.238899\pi\) | |||||||
\(318\) | −20.3000 | −1.13837 | ||||||||
\(319\) | − | 12.4512i | − | 0.697132i | ||||||
\(320\) | 57.4774 | 3.21308 | ||||||||
\(321\) | −2.98968 | −0.166868 | ||||||||
\(322\) | −30.3799 | − | 15.7359i | −1.69300 | − | 0.876929i | ||||
\(323\) | −21.9008 | −1.21859 | ||||||||
\(324\) | 5.27053 | 0.292807 | ||||||||
\(325\) | − | 7.96693i | − | 0.441926i | ||||||
\(326\) | 17.6563 | 0.977891 | ||||||||
\(327\) | 4.45718 | 0.246483 | ||||||||
\(328\) | 44.0932i | 2.43464i | ||||||||
\(329\) | −31.9837 | − | 6.81027i | −1.76332 | − | 0.375462i | ||||
\(330\) | 21.9008 | 1.20560 | ||||||||
\(331\) | −8.65628 | −0.475792 | −0.237896 | − | 0.971291i | \(-0.576458\pi\) | ||||
−0.237896 | + | 0.971291i | \(0.576458\pi\) | |||||||
\(332\) | 83.0489 | 4.55790 | ||||||||
\(333\) | − | 2.90409i | − | 0.159143i | ||||||
\(334\) | − | 59.4017i | − | 3.25032i | ||||||
\(335\) | 20.0892i | 1.09759i | ||||||||
\(336\) | −34.2551 | − | 7.29392i | −1.86877 | − | 0.397916i | ||||
\(337\) | 30.8635i | 1.68124i | 0.541625 | + | 0.840620i | \(0.317809\pi\) | ||||
−0.541625 | + | 0.840620i | \(0.682191\pi\) | |||||||
\(338\) | 24.4188 | 1.32821 | ||||||||
\(339\) | −20.6163 | −1.11973 | ||||||||
\(340\) | −95.1653 | −5.16106 | ||||||||
\(341\) | 8.07957 | 0.437533 | ||||||||
\(342\) | 8.46329 | 0.457642 | ||||||||
\(343\) | −10.9020 | + | 14.9715i | −0.588651 | + | 0.808388i | ||||
\(344\) | − | 6.92842i | − | 0.373556i | ||||||
\(345\) | 11.9669 | + | 3.28781i | 0.644278 | + | 0.177010i | ||||
\(346\) | 53.0010i | 2.84935i | ||||||||
\(347\) | −12.5080 | −0.671464 | −0.335732 | − | 0.941957i | \(-0.608984\pi\) | ||||
−0.335732 | + | 0.941957i | \(0.608984\pi\) | |||||||
\(348\) | − | 20.9078i | − | 1.12078i | ||||||
\(349\) | − | 25.2185i | − | 1.34991i | −0.737857 | − | 0.674957i | \(-0.764162\pi\) | ||
0.737857 | − | 0.674957i | \(-0.235838\pi\) | |||||||
\(350\) | −2.52038 | + | 11.8367i | −0.134720 | + | 0.632697i | ||||
\(351\) | 4.69639 | 0.250675 | ||||||||
\(352\) | 56.6735i | 3.02071i | ||||||||
\(353\) | − | 5.98101i | − | 0.318337i | −0.987251 | − | 0.159169i | \(-0.949119\pi\) | ||
0.987251 | − | 0.159169i | \(-0.0508813\pi\) | |||||||
\(354\) | −8.50799 | −0.452195 | ||||||||
\(355\) | 23.9041 | 1.26870 | ||||||||
\(356\) | 11.5203 | 0.610576 | ||||||||
\(357\) | 18.0561 | + | 3.84468i | 0.955630 | + | 0.203482i | ||||
\(358\) | −25.6563 | −1.35598 | ||||||||
\(359\) | − | 2.58774i | − | 0.136576i | −0.997666 | − | 0.0682878i | \(-0.978246\pi\) | ||
0.997666 | − | 0.0682878i | \(-0.0217536\pi\) | |||||||
\(360\) | 22.8203 | 1.20274 | ||||||||
\(361\) | −9.14828 | −0.481489 | ||||||||
\(362\) | −28.5325 | −1.49963 | ||||||||
\(363\) | − | 1.14828i | − | 0.0602692i | ||||||
\(364\) | −64.0530 | − | 13.6388i | −3.35729 | − | 0.714866i | ||||
\(365\) | − | 24.9879i | − | 1.30793i | ||||||
\(366\) | − | 22.1876i | − | 1.15977i | ||||||
\(367\) | 20.7836 | 1.08490 | 0.542448 | − | 0.840089i | \(-0.317498\pi\) | ||||
0.542448 | + | 0.840089i | \(0.317498\pi\) | |||||||
\(368\) | −16.8186 | + | 61.2163i | −0.876732 | + | 3.19112i | ||||
\(369\) | 5.00000i | 0.260290i | ||||||||
\(370\) | − | 20.2635i | − | 1.05345i | ||||||
\(371\) | 19.4820 | + | 4.14828i | 1.01145 | + | 0.215368i | ||||
\(372\) | 13.5671 | 0.703421 | ||||||||
\(373\) | − | 2.43479i | − | 0.126069i | −0.998011 | − | 0.0630344i | \(-0.979922\pi\) | ||
0.998011 | − | 0.0630344i | \(-0.0200778\pi\) | |||||||
\(374\) | − | 59.0531i | − | 3.05356i | ||||||
\(375\) | 8.54887i | 0.441462i | ||||||||
\(376\) | 108.996i | 5.62103i | ||||||||
\(377\) | − | 18.6302i | − | 0.959507i | ||||||
\(378\) | −6.97756 | − | 1.48573i | −0.358887 | − | 0.0764176i | ||||
\(379\) | 10.3510i | 0.531693i | 0.964015 | + | 0.265846i | \(0.0856514\pi\) | ||||
−0.964015 | + | 0.265846i | \(0.914349\pi\) | |||||||
\(380\) | 42.8086 | 2.19604 | ||||||||
\(381\) | − | 19.0561i | − | 0.976274i | ||||||
\(382\) | 32.3183i | 1.65355i | ||||||||
\(383\) | −4.93695 | −0.252266 | −0.126133 | − | 0.992013i | \(-0.540257\pi\) | ||||
−0.126133 | + | 0.992013i | \(0.540257\pi\) | |||||||
\(384\) | 23.7785i | 1.21344i | ||||||||
\(385\) | −21.0183 | − | 4.47541i | −1.07119 | − | 0.228088i | ||||
\(386\) | −8.00000 | −0.407189 | ||||||||
\(387\) | − | 0.785656i | − | 0.0399372i | ||||||
\(388\) | −40.8203 | −2.07233 | ||||||||
\(389\) | 15.7572i | 0.798922i | 0.916750 | + | 0.399461i | \(0.130803\pi\) | ||||
−0.916750 | + | 0.399461i | \(0.869197\pi\) | |||||||
\(390\) | 32.7694 | 1.65934 | ||||||||
\(391\) | 8.86523 | − | 32.2675i | 0.448334 | − | 1.63184i | ||||
\(392\) | 56.3757 | + | 25.1483i | 2.84740 | + | 1.27018i | ||||
\(393\) | −10.1483 | −0.511913 | ||||||||
\(394\) | −45.6413 | −2.29938 | ||||||||
\(395\) | 3.89183i | 0.195819i | ||||||||
\(396\) | 16.5429i | 0.831310i | ||||||||
\(397\) | 10.4890i | 0.526428i | 0.964737 | + | 0.263214i | \(0.0847826\pi\) | ||||
−0.964737 | + | 0.263214i | \(0.915217\pi\) | |||||||
\(398\) | 41.0019 | 2.05524 | ||||||||
\(399\) | −8.12225 | − | 1.72947i | −0.406621 | − | 0.0865816i | ||||
\(400\) | 22.4559 | 1.12280 | ||||||||
\(401\) | − | 20.9962i | − | 1.04850i | −0.851565 | − | 0.524249i | \(-0.824346\pi\) | ||
0.851565 | − | 0.524249i | \(-0.175654\pi\) | |||||||
\(402\) | −20.9327 | −1.04403 | ||||||||
\(403\) | 12.0892 | 0.602205 | ||||||||
\(404\) | − | 38.9268i | − | 1.93668i | ||||||
\(405\) | 2.58774 | 0.128586 | ||||||||
\(406\) | −5.89377 | + | 27.6795i | −0.292503 | + | 1.37371i | ||||
\(407\) | 9.11521 | 0.451824 | ||||||||
\(408\) | − | 61.5326i | − | 3.04632i | ||||||
\(409\) | − | 14.1453i | − | 0.699439i | −0.936854 | − | 0.349720i | \(-0.886277\pi\) | ||
0.936854 | − | 0.349720i | \(-0.113723\pi\) | |||||||
\(410\) | 34.8878i | 1.72299i | ||||||||
\(411\) | −4.71006 | −0.232330 | ||||||||
\(412\) | 28.5143 | 1.40480 | ||||||||
\(413\) | 8.16516 | + | 1.73860i | 0.401781 | + | 0.0855510i | ||||
\(414\) | −3.42586 | + | 12.4694i | −0.168372 | + | 0.612837i | ||||
\(415\) | 40.7755 | 2.00159 | ||||||||
\(416\) | 84.7986i | 4.15759i | ||||||||
\(417\) | −2.43290 | −0.119140 | ||||||||
\(418\) | 26.5641i | 1.29929i | ||||||||
\(419\) | 20.9145 | 1.02174 | 0.510869 | − | 0.859659i | \(-0.329324\pi\) | ||||
0.510869 | + | 0.859659i | \(0.329324\pi\) | |||||||
\(420\) | −35.2936 | − | 7.51504i | −1.72215 | − | 0.366696i | ||||
\(421\) | 1.41837i | 0.0691269i | 0.999403 | + | 0.0345635i | \(0.0110041\pi\) | ||||
−0.999403 | + | 0.0345635i | \(0.988996\pi\) | |||||||
\(422\) | −49.5942 | −2.41421 | ||||||||
\(423\) | 12.3597i | 0.600950i | ||||||||
\(424\) | − | 66.3917i | − | 3.22427i | ||||||
\(425\) | −11.8367 | −0.574163 | ||||||||
\(426\) | 24.9078i | 1.20679i | ||||||||
\(427\) | −4.53403 | + | 21.2936i | −0.219417 | + | 1.03047i | ||||
\(428\) | − | 15.7572i | − | 0.761653i | ||||||
\(429\) | 14.7408i | 0.711691i | ||||||||
\(430\) | − | 5.48196i | − | 0.264364i | ||||||
\(431\) | 25.0283i | 1.20557i | 0.797904 | + | 0.602784i | \(0.205942\pi\) | ||||
−0.797904 | + | 0.602784i | \(0.794058\pi\) | |||||||
\(432\) | 13.2375i | 0.636888i | ||||||||
\(433\) | 26.8717 | 1.29137 | 0.645686 | − | 0.763603i | \(-0.276571\pi\) | ||||
0.645686 | + | 0.763603i | \(0.276571\pi\) | |||||||
\(434\) | −17.9612 | − | 3.82447i | −0.862166 | − | 0.183581i | ||||
\(435\) | − | 10.2654i | − | 0.492187i | ||||||
\(436\) | 23.4917i | 1.12505i | ||||||||
\(437\) | −3.98788 | + | 14.5150i | −0.190766 | + | 0.694348i | ||||
\(438\) | 26.0371 | 1.24410 | ||||||||
\(439\) | − | 20.3898i | − | 0.973151i | −0.873638 | − | 0.486576i | \(-0.838246\pi\) | ||
0.873638 | − | 0.486576i | \(-0.161754\pi\) | |||||||
\(440\) | 71.6272i | 3.41470i | ||||||||
\(441\) | 6.39279 | + | 2.85172i | 0.304418 | + | 0.135796i | ||||
\(442\) | − | 88.3591i | − | 4.20281i | ||||||
\(443\) | −19.3787 | −0.920710 | −0.460355 | − | 0.887735i | \(-0.652278\pi\) | ||||
−0.460355 | + | 0.887735i | \(0.652278\pi\) | |||||||
\(444\) | 15.3061 | 0.726397 | ||||||||
\(445\) | 5.65628 | 0.268133 | ||||||||
\(446\) | − | 8.15937i | − | 0.386357i | ||||||
\(447\) | 19.6634 | 0.930046 | ||||||||
\(448\) | 12.2386 | − | 57.4774i | 0.578221 | − | 2.71555i | ||||
\(449\) | −14.9599 | −0.706001 | −0.353000 | − | 0.935623i | \(-0.614839\pi\) | ||||
−0.353000 | + | 0.935623i | \(0.614839\pi\) | |||||||
\(450\) | 4.57414 | 0.215627 | ||||||||
\(451\) | −15.6937 | −0.738989 | ||||||||
\(452\) | − | 108.659i | − | 5.11089i | ||||||
\(453\) | − | 4.72242i | − | 0.221879i | ||||||
\(454\) | −23.0020 | −1.07954 | ||||||||
\(455\) | −31.4489 | − | 6.69639i | −1.47435 | − | 0.313932i | ||||
\(456\) | 27.6795i | 1.29621i | ||||||||
\(457\) | 26.5957i | 1.24409i | 0.782980 | + | 0.622047i | \(0.213699\pi\) | ||||
−0.782980 | + | 0.622047i | \(0.786301\pi\) | |||||||
\(458\) | −29.2143 | −1.36510 | ||||||||
\(459\) | − | 6.97756i | − | 0.325685i | ||||||
\(460\) | −17.3285 | + | 63.0721i | −0.807946 | + | 2.94075i | ||||
\(461\) | − | 23.7736i | − | 1.10725i | −0.832767 | − | 0.553624i | \(-0.813244\pi\) | ||
0.832767 | − | 0.553624i | \(-0.186756\pi\) | |||||||
\(462\) | 4.66332 | − | 21.9008i | 0.216957 | − | 1.01892i | ||||
\(463\) | 26.3407 | 1.22416 | 0.612079 | − | 0.790797i | \(-0.290334\pi\) | ||||
0.612079 | + | 0.790797i | \(0.290334\pi\) | |||||||
\(464\) | 52.5120 | 2.43781 | ||||||||
\(465\) | 6.66121 | 0.308906 | ||||||||
\(466\) | 24.9970 | 1.15796 | ||||||||
\(467\) | 9.18158 | 0.424873 | 0.212436 | − | 0.977175i | \(-0.431860\pi\) | ||||
0.212436 | + | 0.977175i | \(0.431860\pi\) | |||||||
\(468\) | 24.7525i | 1.14418i | ||||||||
\(469\) | 20.0892 | + | 4.27758i | 0.927632 | + | 0.197520i | ||||
\(470\) | 86.2406i | 3.97798i | ||||||||
\(471\) | − | 9.48360i | − | 0.436981i | ||||||
\(472\) | − | 27.8257i | − | 1.28078i | ||||||
\(473\) | 2.46597 | 0.113386 | ||||||||
\(474\) | −4.05524 | −0.186263 | ||||||||
\(475\) | 5.32454 | 0.244307 | ||||||||
\(476\) | −20.2635 | + | 95.1653i | −0.928776 | + | 4.36190i | ||||
\(477\) | − | 7.52857i | − | 0.344709i | ||||||
\(478\) | 32.0271 | 1.46488 | ||||||||
\(479\) | 2.73292 | 0.124871 | 0.0624353 | − | 0.998049i | \(-0.480113\pi\) | ||||
0.0624353 | + | 0.998049i | \(0.480113\pi\) | |||||||
\(480\) | 46.7245i | 2.13267i | ||||||||
\(481\) | 13.6388 | 0.621874 | ||||||||
\(482\) | 49.8671 | 2.27138 | ||||||||
\(483\) | 5.83592 | − | 11.2669i | 0.265544 | − | 0.512660i | ||||
\(484\) | 6.05206 | 0.275094 | ||||||||
\(485\) | −20.0420 | −0.910061 | ||||||||
\(486\) | 2.69639i | 0.122311i | ||||||||
\(487\) | 21.3738 | 0.968539 | 0.484270 | − | 0.874919i | \(-0.339085\pi\) | ||||
0.484270 | + | 0.874919i | \(0.339085\pi\) | |||||||
\(488\) | 72.5654 | 3.28488 | ||||||||
\(489\) | 6.54811i | 0.296116i | ||||||||
\(490\) | 44.6060 | + | 19.8980i | 2.01510 | + | 0.898901i | ||||
\(491\) | −21.7785 | −0.982851 | −0.491426 | − | 0.870920i | \(-0.663524\pi\) | ||||
−0.491426 | + | 0.870920i | \(0.663524\pi\) | |||||||
\(492\) | −26.3527 | −1.18807 | ||||||||
\(493\) | −27.6795 | −1.24662 | ||||||||
\(494\) | 39.7469i | 1.78830i | ||||||||
\(495\) | 8.12225i | 0.365068i | ||||||||
\(496\) | 34.0751i | 1.53002i | ||||||||
\(497\) | 5.08989 | − | 23.9041i | 0.228313 | − | 1.07225i | ||||
\(498\) | 42.4876i | 1.90392i | ||||||||
\(499\) | −18.1223 | −0.811263 | −0.405632 | − | 0.914037i | \(-0.632948\pi\) | ||||
−0.405632 | + | 0.914037i | \(0.632948\pi\) | |||||||
\(500\) | −45.0571 | −2.01502 | ||||||||
\(501\) | 22.0301 | 0.984231 | ||||||||
\(502\) | −57.5265 | −2.56753 | ||||||||
\(503\) | −15.1427 | −0.675180 | −0.337590 | − | 0.941293i | \(-0.609612\pi\) | ||||
−0.337590 | + | 0.941293i | \(0.609612\pi\) | |||||||
\(504\) | 4.85912 | − | 22.8203i | 0.216443 | − | 1.01650i | ||||
\(505\) | − | 19.1124i | − | 0.850490i | ||||||
\(506\) | −39.1382 | − | 10.7529i | −1.73991 | − | 0.478025i | ||||
\(507\) | 9.05611i | 0.402196i | ||||||||
\(508\) | 100.436 | 4.45612 | ||||||||
\(509\) | − | 32.2274i | − | 1.42846i | −0.699913 | − | 0.714228i | \(-0.746778\pi\) | ||
0.699913 | − | 0.714228i | \(-0.253222\pi\) | |||||||
\(510\) | − | 48.6864i | − | 2.15587i | ||||||
\(511\) | −24.9879 | − | 5.32066i | −1.10540 | − | 0.235372i | ||||
\(512\) | −5.54407 | −0.245015 | ||||||||
\(513\) | 3.13874i | 0.138579i | ||||||||
\(514\) | − | 40.9780i | − | 1.80746i | ||||||
\(515\) | 14.0000 | 0.616914 | ||||||||
\(516\) | 4.14083 | 0.182290 | ||||||||
\(517\) | −38.7940 | −1.70616 | ||||||||
\(518\) | −20.2635 | − | 4.31469i | −0.890327 | − | 0.189577i | ||||
\(519\) | −19.6563 | −0.862815 | ||||||||
\(520\) | 107.173i | 4.69986i | ||||||||
\(521\) | 12.9878 | 0.569007 | 0.284504 | − | 0.958675i | \(-0.408171\pi\) | ||||
0.284504 | + | 0.958675i | \(0.408171\pi\) | |||||||
\(522\) | 10.6964 | 0.468168 | ||||||||
\(523\) | −19.6998 | −0.861413 | −0.430707 | − | 0.902492i | \(-0.641736\pi\) | ||||
−0.430707 | + | 0.902492i | \(0.641736\pi\) | |||||||
\(524\) | − | 53.4869i | − | 2.33658i | ||||||
\(525\) | −4.38982 | − | 0.934722i | −0.191588 | − | 0.0407946i | ||||
\(526\) | − | 41.0510i | − | 1.78991i | ||||||
\(527\) | − | 17.9612i | − | 0.782403i | ||||||
\(528\) | −41.5490 | −1.80819 | ||||||||
\(529\) | −19.7715 | − | 11.7511i | −0.859630 | − | 0.510917i | ||||
\(530\) | − | 52.5310i | − | 2.28180i | ||||||
\(531\) | − | 3.15532i | − | 0.136929i | ||||||
\(532\) | 9.11521 | − | 42.8086i | 0.395194 | − | 1.85599i | ||||
\(533\) | −23.4820 | −1.01712 | ||||||||
\(534\) | 5.89377i | 0.255048i | ||||||||
\(535\) | − | 7.73651i | − | 0.334478i | ||||||
\(536\) | − | 68.4610i | − | 2.95707i | ||||||
\(537\) | − | 9.51504i | − | 0.410604i | ||||||
\(538\) | − | 52.7094i | − | 2.27246i | ||||||
\(539\) | −8.95081 | + | 20.0653i | −0.385539 | + | 0.864275i | ||||
\(540\) | 13.6388i | 0.586919i | ||||||||
\(541\) | −13.5882 | −0.584203 | −0.292102 | − | 0.956387i | \(-0.594355\pi\) | ||||
−0.292102 | + | 0.956387i | \(0.594355\pi\) | |||||||
\(542\) | − | 24.5782i | − | 1.05572i | ||||||
\(543\) | − | 10.5817i | − | 0.454105i | ||||||
\(544\) | 125.988 | 5.40167 | ||||||||
\(545\) | 11.5340i | 0.494063i | ||||||||
\(546\) | 6.97756 | − | 32.7694i | 0.298612 | − | 1.40240i | ||||
\(547\) | −3.58118 | −0.153120 | −0.0765602 | − | 0.997065i | \(-0.524394\pi\) | ||||
−0.0765602 | + | 0.997065i | \(0.524394\pi\) | |||||||
\(548\) | − | 24.8245i | − | 1.06045i | ||||||
\(549\) | 8.22864 | 0.351190 | ||||||||
\(550\) | 14.3571i | 0.612187i | ||||||||
\(551\) | 12.4512 | 0.530438 | ||||||||
\(552\) | −40.7816 | − | 11.2044i | −1.73578 | − | 0.476890i | ||||
\(553\) | 3.89183 | + | 0.828686i | 0.165498 | + | 0.0352393i | ||||
\(554\) | 56.8135 | 2.41377 | ||||||||
\(555\) | 7.51504 | 0.318996 | ||||||||
\(556\) | − | 12.8227i | − | 0.543803i | ||||||
\(557\) | 19.7269i | 0.835854i | 0.908481 | + | 0.417927i | \(0.137243\pi\) | ||||
−0.908481 | + | 0.417927i | \(0.862757\pi\) | |||||||
\(558\) | 6.94090i | 0.293832i | ||||||||
\(559\) | 3.68975 | 0.156060 | ||||||||
\(560\) | 18.8747 | − | 88.6432i | 0.797604 | − | 3.74586i | ||||
\(561\) | 21.9008 | 0.924652 | ||||||||
\(562\) | − | 35.9225i | − | 1.51530i | ||||||
\(563\) | −27.5939 | −1.16294 | −0.581472 | − | 0.813567i | \(-0.697523\pi\) | ||||
−0.581472 | + | 0.813567i | \(0.697523\pi\) | |||||||
\(564\) | −65.1423 | −2.74299 | ||||||||
\(565\) | − | 53.3497i | − | 2.24444i | ||||||
\(566\) | −2.74069 | −0.115200 | ||||||||
\(567\) | 0.551006 | − | 2.58774i | 0.0231401 | − | 0.108675i | ||||
\(568\) | −81.4619 | −3.41806 | ||||||||
\(569\) | − | 20.6307i | − | 0.864883i | −0.901662 | − | 0.432441i | \(-0.857652\pi\) | ||
0.901662 | − | 0.432441i | \(-0.142348\pi\) | |||||||
\(570\) | 21.9008i | 0.917323i | ||||||||
\(571\) | − | 32.8185i | − | 1.37341i | −0.726935 | − | 0.686706i | \(-0.759056\pi\) | ||
0.726935 | − | 0.686706i | \(-0.240944\pi\) | |||||||
\(572\) | −77.6918 | −3.24846 | ||||||||
\(573\) | −11.9857 | −0.500712 | ||||||||
\(574\) | 34.8878 | + | 7.42864i | 1.45619 | + | 0.310065i | ||||
\(575\) | −2.15532 | + | 7.84492i | −0.0898833 | + | 0.327156i | ||||
\(576\) | −22.2114 | −0.925476 | ||||||||
\(577\) | 5.63729i | 0.234683i | 0.993092 | + | 0.117342i | \(0.0374373\pi\) | ||||
−0.993092 | + | 0.117342i | \(0.962563\pi\) | |||||||
\(578\) | −85.4388 | −3.55379 | ||||||||
\(579\) | − | 2.96693i | − | 0.123301i | ||||||
\(580\) | 54.1040 | 2.24655 | ||||||||
\(581\) | 8.68231 | − | 40.7755i | 0.360203 | − | 1.69165i | ||||
\(582\) | − | 20.8835i | − | 0.865651i | ||||||
\(583\) | 23.6302 | 0.978665 | ||||||||
\(584\) | 85.1553i | 3.52375i | ||||||||
\(585\) | 12.1530i | 0.502466i | ||||||||
\(586\) | 19.7998 | 0.817920 | ||||||||
\(587\) | 27.6633i | 1.14179i | 0.821024 | + | 0.570894i | \(0.193403\pi\) | ||||
−0.821024 | + | 0.570894i | \(0.806597\pi\) | |||||||
\(588\) | −15.0301 | + | 33.6934i | −0.619830 | + | 1.38949i | ||||
\(589\) | 8.07957i | 0.332913i | ||||||||
\(590\) | − | 22.0165i | − | 0.906404i | ||||||
\(591\) | − | 16.9268i | − | 0.696276i | ||||||
\(592\) | 38.4428i | 1.57999i | ||||||||
\(593\) | 36.7194i | 1.50789i | 0.656940 | + | 0.753943i | \(0.271851\pi\) | ||||
−0.656940 | + | 0.753943i | \(0.728149\pi\) | |||||||
\(594\) | −8.46329 | −0.347253 | ||||||||
\(595\) | −9.94902 | + | 46.7245i | −0.407870 | + | 1.91552i | ||||
\(596\) | 103.637i | 4.24512i | ||||||||
\(597\) | 15.2062i | 0.622348i | ||||||||
\(598\) | −58.5612 | − | 16.0892i | −2.39474 | − | 0.657935i | ||||
\(599\) | 18.3337 | 0.749094 | 0.374547 | − | 0.927208i | \(-0.377798\pi\) | ||||
0.374547 | + | 0.927208i | \(0.377798\pi\) | |||||||
\(600\) | 14.9599i | 0.610735i | ||||||||
\(601\) | 41.6272i | 1.69801i | 0.528384 | + | 0.849005i | \(0.322798\pi\) | ||||
−0.528384 | + | 0.849005i | \(0.677202\pi\) | |||||||
\(602\) | −5.48196 | − | 1.16727i | −0.223428 | − | 0.0475744i | ||||
\(603\) | − | 7.76322i | − | 0.316143i | ||||||
\(604\) | 24.8897 | 1.01275 | ||||||||
\(605\) | 2.97146 | 0.120807 | ||||||||
\(606\) | 19.9149 | 0.808986 | ||||||||
\(607\) | 10.7625i | 0.436838i | 0.975855 | + | 0.218419i | \(0.0700899\pi\) | ||||
−0.975855 | + | 0.218419i | \(0.929910\pi\) | |||||||
\(608\) | −56.6735 | −2.29841 | ||||||||
\(609\) | −10.2654 | − | 2.18580i | −0.415974 | − | 0.0885730i | ||||
\(610\) | 57.4158 | 2.32470 | ||||||||
\(611\) | −58.0461 | −2.34829 | ||||||||
\(612\) | 36.7755 | 1.48656 | ||||||||
\(613\) | − | 30.2181i | − | 1.22050i | −0.792210 | − | 0.610248i | \(-0.791070\pi\) | ||
0.792210 | − | 0.610248i | \(-0.208930\pi\) | |||||||
\(614\) | − | 26.9127i | − | 1.08611i | ||||||
\(615\) | −12.9387 | −0.521739 | ||||||||
\(616\) | 71.6272 | + | 15.2515i | 2.88594 | + | 0.614502i | ||||
\(617\) | 35.6061i | 1.43345i | 0.697357 | + | 0.716724i | \(0.254359\pi\) | ||||
−0.697357 | + | 0.716724i | \(0.745641\pi\) | |||||||
\(618\) | 14.5878i | 0.586809i | ||||||||
\(619\) | −5.02253 | −0.201873 | −0.100936 | − | 0.994893i | \(-0.532184\pi\) | ||||
−0.100936 | + | 0.994893i | \(0.532184\pi\) | |||||||
\(620\) | 35.1081i | 1.40998i | ||||||||
\(621\) | −4.62447 | − | 1.27053i | −0.185574 | − | 0.0509848i | ||||
\(622\) | − | 26.8558i | − | 1.07682i | ||||||
\(623\) | 1.20439 | − | 5.65628i | 0.0482528 | − | 0.226614i | ||||
\(624\) | −62.1683 | −2.48872 | ||||||||
\(625\) | −30.6042 | −1.22417 | ||||||||
\(626\) | −53.0202 | −2.11911 | ||||||||
\(627\) | −9.85172 | −0.393440 | ||||||||
\(628\) | 49.9836 | 1.99456 | ||||||||
\(629\) | − | 20.2635i | − | 0.807958i | ||||||
\(630\) | 3.84468 | − | 18.0561i | 0.153176 | − | 0.719372i | ||||
\(631\) | − | 48.3736i | − | 1.92572i | −0.269995 | − | 0.962862i | \(-0.587022\pi\) | ||
0.269995 | − | 0.962862i | \(-0.412978\pi\) | |||||||
\(632\) | − | 13.2628i | − | 0.527566i | ||||||
\(633\) | − | 18.3928i | − | 0.731048i | ||||||
\(634\) | −70.2195 | −2.78877 | ||||||||
\(635\) | 49.3122 | 1.95690 | ||||||||
\(636\) | 39.6796 | 1.57340 | ||||||||
\(637\) | −13.3928 | + | 30.0230i | −0.530641 | + | 1.18956i | ||||
\(638\) | 33.5732i | 1.32918i | ||||||||
\(639\) | −9.23746 | −0.365428 | ||||||||
\(640\) | −61.5326 | −2.43229 | ||||||||
\(641\) | 18.9142i | 0.747065i | 0.927617 | + | 0.373532i | \(0.121854\pi\) | ||||
−0.927617 | + | 0.373532i | \(0.878146\pi\) | |||||||
\(642\) | 8.06135 | 0.318156 | ||||||||
\(643\) | −2.88975 | −0.113961 | −0.0569803 | − | 0.998375i | \(-0.518147\pi\) | ||||
−0.0569803 | + | 0.998375i | \(0.518147\pi\) | |||||||
\(644\) | 59.3823 | + | 30.7584i | 2.33999 | + | 1.21205i | ||||
\(645\) | 2.03307 | 0.0800522 | ||||||||
\(646\) | 59.0531 | 2.32341 | ||||||||
\(647\) | − | 3.95798i | − | 0.155604i | −0.996969 | − | 0.0778021i | \(-0.975210\pi\) | ||
0.996969 | − | 0.0778021i | \(-0.0247902\pi\) | |||||||
\(648\) | −8.81864 | −0.346429 | ||||||||
\(649\) | 9.90376 | 0.388757 | ||||||||
\(650\) | 21.4820i | 0.842592i | ||||||||
\(651\) | 1.41837 | − | 6.66121i | 0.0555902 | − | 0.261073i | ||||
\(652\) | −34.5120 | −1.35160 | ||||||||
\(653\) | −14.9219 | −0.583939 | −0.291970 | − | 0.956428i | \(-0.594311\pi\) | ||||
−0.291970 | + | 0.956428i | \(0.594311\pi\) | |||||||
\(654\) | −12.0183 | −0.469953 | ||||||||
\(655\) | − | 26.2611i | − | 1.02611i | ||||||
\(656\) | − | 66.1873i | − | 2.58418i | ||||||
\(657\) | 9.65628i | 0.376727i | ||||||||
\(658\) | 86.2406 | + | 18.3632i | 3.36201 | + | 0.715871i | ||||
\(659\) | 6.64298i | 0.258774i | 0.991594 | + | 0.129387i | \(0.0413009\pi\) | ||||
−0.991594 | + | 0.129387i | \(0.958699\pi\) | |||||||
\(660\) | −42.8086 | −1.66632 | ||||||||
\(661\) | 3.57160 | 0.138919 | 0.0694595 | − | 0.997585i | \(-0.477873\pi\) | ||||
0.0694595 | + | 0.997585i | \(0.477873\pi\) | |||||||
\(662\) | 23.3407 | 0.907163 | ||||||||
\(663\) | 32.7694 | 1.27266 | ||||||||
\(664\) | −138.957 | −5.39258 | ||||||||
\(665\) | 4.47541 | − | 21.0183i | 0.173549 | − | 0.815053i | ||||
\(666\) | 7.83058i | 0.303429i | ||||||||
\(667\) | −5.04012 | + | 18.3449i | −0.195154 | + | 0.710319i | ||||
\(668\) | 116.110i | 4.49244i | ||||||||
\(669\) | 3.02603 | 0.116993 | ||||||||
\(670\) | − | 54.1683i | − | 2.09270i | ||||||
\(671\) | 25.8276i | 0.997063i | ||||||||
\(672\) | 46.7245 | + | 9.94902i | 1.80244 | + | 0.383792i | ||||
\(673\) | −7.91786 | −0.305211 | −0.152606 | − | 0.988287i | \(-0.548766\pi\) | ||||
−0.152606 | + | 0.988287i | \(0.548766\pi\) | |||||||
\(674\) | − | 83.2200i | − | 3.20552i | ||||||
\(675\) | 1.69639i | 0.0652942i | ||||||||
\(676\) | −47.7305 | −1.83579 | ||||||||
\(677\) | 15.6794 | 0.602608 | 0.301304 | − | 0.953528i | \(-0.402578\pi\) | ||||
0.301304 | + | 0.953528i | \(0.402578\pi\) | |||||||
\(678\) | 55.5897 | 2.13491 | ||||||||
\(679\) | −4.26754 | + | 20.0420i | −0.163773 | + | 0.769142i | ||||
\(680\) | 159.230 | 6.10621 | ||||||||
\(681\) | − | 8.53065i | − | 0.326895i | ||||||
\(682\) | −21.7857 | −0.834218 | ||||||||
\(683\) | 18.6864 | 0.715013 | 0.357507 | − | 0.933911i | \(-0.383627\pi\) | ||||
0.357507 | + | 0.933911i | \(0.383627\pi\) | |||||||
\(684\) | −16.5429 | −0.632532 | ||||||||
\(685\) | − | 12.1884i | − | 0.465695i | ||||||
\(686\) | 29.3960 | − | 40.3692i | 1.12234 | − | 1.54130i | ||||
\(687\) | − | 10.8346i | − | 0.413366i | ||||||
\(688\) | 10.4001i | 0.396500i | ||||||||
\(689\) | 35.3571 | 1.34700 | ||||||||
\(690\) | −32.2675 | − | 8.86523i | −1.22840 | − | 0.337493i | ||||
\(691\) | − | 32.0089i | − | 1.21768i | −0.793294 | − | 0.608839i | \(-0.791636\pi\) | ||
0.793294 | − | 0.608839i | \(-0.208364\pi\) | |||||||
\(692\) | − | 103.599i | − | 3.93825i | ||||||
\(693\) | 8.12225 | + | 1.72947i | 0.308539 | + | 0.0656970i | ||||
\(694\) | 33.7265 | 1.28024 | ||||||||
\(695\) | − | 6.29571i | − | 0.238810i | ||||||
\(696\) | 34.9829i | 1.32602i | ||||||||
\(697\) | 34.8878i | 1.32147i | ||||||||
\(698\) | 67.9989i | 2.57380i | ||||||||
\(699\) | 9.27053i | 0.350644i | ||||||||
\(700\) | 4.92648 | − | 23.1367i | 0.186204 | − | 0.874485i | ||||
\(701\) | 2.81463i | 0.106307i | 0.998586 | + | 0.0531535i | \(0.0169273\pi\) | ||||
−0.998586 | + | 0.0531535i | \(0.983073\pi\) | |||||||
\(702\) | −12.6633 | −0.477946 | ||||||||
\(703\) | 9.11521i | 0.343787i | ||||||||
\(704\) | − | 69.7160i | − | 2.62752i | ||||||
\(705\) | −31.9837 | −1.20458 | ||||||||
\(706\) | 16.1272i | 0.606954i | ||||||||
\(707\) | −19.1124 | − | 4.06959i | −0.718795 | − | 0.153053i | ||||
\(708\) | 16.6302 | 0.625003 | ||||||||
\(709\) | − | 3.45898i | − | 0.129905i | −0.997888 | − | 0.0649524i | \(-0.979310\pi\) | ||
0.997888 | − | 0.0649524i | \(-0.0206895\pi\) | |||||||
\(710\) | −64.4549 | −2.41895 | ||||||||
\(711\) | − | 1.50395i | − | 0.0564026i | ||||||
\(712\) | −19.2758 | −0.722391 | ||||||||
\(713\) | −11.9040 | − | 3.27053i | −0.445810 | − | 0.122482i | ||||
\(714\) | −48.6864 | − | 10.3668i | −1.82204 | − | 0.387966i | ||||
\(715\) | −38.1453 | −1.42655 | ||||||||
\(716\) | 50.1493 | 1.87417 | ||||||||
\(717\) | 11.8777i | 0.443583i | ||||||||
\(718\) | 6.97756i | 0.260400i | ||||||||
\(719\) | 2.89888i | 0.108110i | 0.998538 | + | 0.0540549i | \(0.0172146\pi\) | ||||
−0.998538 | + | 0.0540549i | \(0.982785\pi\) | |||||||
\(720\) | −34.2551 | −1.27661 | ||||||||
\(721\) | 2.98101 | − | 14.0000i | 0.111019 | − | 0.521387i | ||||
\(722\) | 24.6674 | 0.918024 | ||||||||
\(723\) | 18.4940i | 0.687800i | ||||||||
\(724\) | 55.7713 | 2.07273 | ||||||||
\(725\) | 6.72947 | 0.249926 | ||||||||
\(726\) | 3.09622i | 0.114912i | ||||||||
\(727\) | 48.9506 | 1.81548 | 0.907739 | − | 0.419536i | \(-0.137807\pi\) | ||||
0.907739 | + | 0.419536i | \(0.137807\pi\) | |||||||
\(728\) | 107.173 | + | 22.8203i | 3.97211 | + | 0.845778i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 67.3773i | 2.49374i | ||||||||
\(731\) | − | 5.48196i | − | 0.202758i | ||||||
\(732\) | 43.3693i | 1.60298i | ||||||||
\(733\) | −43.2655 | −1.59805 | −0.799024 | − | 0.601299i | \(-0.794650\pi\) | ||||
−0.799024 | + | 0.601299i | \(0.794650\pi\) | |||||||
\(734\) | −56.0408 | −2.06850 | ||||||||
\(735\) | −7.37950 | + | 16.5429i | −0.272197 | + | 0.610193i | ||||
\(736\) | 22.9409 | − | 83.5000i | 0.845613 | − | 3.07785i | ||||
\(737\) | 24.3668 | 0.897561 | ||||||||
\(738\) | − | 13.4820i | − | 0.496278i | ||||||
\(739\) | 51.0111 | 1.87647 | 0.938237 | − | 0.345994i | \(-0.112458\pi\) | ||||
0.938237 | + | 0.345994i | \(0.112458\pi\) | |||||||
\(740\) | 39.6083i | 1.45603i | ||||||||
\(741\) | −14.7408 | −0.541516 | ||||||||
\(742\) | −52.5310 | − | 11.1854i | −1.92847 | − | 0.410629i | ||||
\(743\) | 11.9002i | 0.436575i | 0.975885 | + | 0.218287i | \(0.0700470\pi\) | ||||
−0.975885 | + | 0.218287i | \(0.929953\pi\) | |||||||
\(744\) | −22.7004 | −0.832238 | ||||||||
\(745\) | 50.8837i | 1.86423i | ||||||||
\(746\) | 6.56516i | 0.240368i | ||||||||
\(747\) | −15.7572 | −0.576526 | ||||||||
\(748\) | 115.429i | 4.22050i | ||||||||
\(749\) | −7.73651 | − | 1.64733i | −0.282686 | − | 0.0601921i | ||||
\(750\) | − | 23.0511i | − | 0.841708i | ||||||
\(751\) | 3.82447i | 0.139557i | 0.997563 | + | 0.0697785i | \(0.0222292\pi\) | ||||
−0.997563 | + | 0.0697785i | \(0.977771\pi\) | |||||||
\(752\) | − | 163.611i | − | 5.96629i | ||||||
\(753\) | − | 21.3346i | − | 0.777477i | ||||||
\(754\) | 50.2345i | 1.82943i | ||||||||
\(755\) | 12.2204 | 0.444746 | ||||||||
\(756\) | 13.6388 | + | 2.90409i | 0.496037 | + | 0.105621i | ||||
\(757\) | − | 14.3935i | − | 0.523141i | −0.965184 | − | 0.261570i | \(-0.915760\pi\) | ||
0.965184 | − | 0.261570i | \(-0.0842404\pi\) | |||||||
\(758\) | − | 27.9102i | − | 1.01375i | ||||||
\(759\) | 3.98788 | − | 14.5150i | 0.144751 | − | 0.526862i | ||||
\(760\) | −71.6272 | −2.59819 | ||||||||
\(761\) | 26.1814i | 0.949073i | 0.880236 | + | 0.474537i | \(0.157384\pi\) | ||||
−0.880236 | + | 0.474537i | \(0.842616\pi\) | |||||||
\(762\) | 51.3827i | 1.86140i | ||||||||
\(763\) | 11.5340 | + | 2.45593i | 0.417560 | + | 0.0889107i | ||||
\(764\) | − | 63.1713i | − | 2.28546i | ||||||
\(765\) | 18.0561 | 0.652820 | ||||||||
\(766\) | 13.3119 | 0.480980 | ||||||||
\(767\) | 14.8186 | 0.535070 | ||||||||
\(768\) | − | 19.6934i | − | 0.710624i | ||||||
\(769\) | −39.1998 | −1.41358 | −0.706790 | − | 0.707423i | \(-0.749858\pi\) | ||||
−0.706790 | + | 0.707423i | \(0.749858\pi\) | |||||||
\(770\) | 56.6735 | + | 12.0675i | 2.04237 | + | 0.434881i | ||||
\(771\) | 15.1973 | 0.547319 | ||||||||
\(772\) | 15.6373 | 0.562798 | ||||||||
\(773\) | 55.1204 | 1.98254 | 0.991272 | − | 0.131835i | \(-0.0420868\pi\) | ||||
0.991272 | + | 0.131835i | \(0.0420868\pi\) | |||||||
\(774\) | 2.11844i | 0.0761457i | ||||||||
\(775\) | 4.36675i | 0.156858i | ||||||||
\(776\) | 68.3003 | 2.45184 | ||||||||
\(777\) | 1.60017 | − | 7.51504i | 0.0574059 | − | 0.269600i | ||||
\(778\) | − | 42.4876i | − | 1.52325i | ||||||
\(779\) | − | 15.6937i | − | 0.562286i | ||||||
\(780\) | −64.0530 | −2.29347 | ||||||||
\(781\) | − | 28.9940i | − | 1.03749i | ||||||
\(782\) | −23.9041 | + | 87.0059i | −0.854810 | + | 3.11133i | ||||
\(783\) | 3.96693i | 0.141766i | ||||||||
\(784\) | −84.6242 | − | 37.7495i | −3.02229 | − | 1.34820i | ||||
\(785\) | 24.5411 | 0.875908 | ||||||||
\(786\) | 27.3638 | 0.976033 | ||||||||
\(787\) | 37.0466 | 1.32057 | 0.660284 | − | 0.751016i | \(-0.270436\pi\) | ||||
0.660284 | + | 0.751016i | \(0.270436\pi\) | |||||||
\(788\) | 89.2133 | 3.17809 | ||||||||
\(789\) | 15.2244 | 0.542004 | ||||||||
\(790\) | − | 10.4939i | − | 0.373357i | ||||||
\(791\) | −53.3497 | − | 11.3597i | −1.89690 | − | 0.403905i | ||||
\(792\) | − | 27.6795i | − | 0.983547i | ||||||
\(793\) | 38.6449i | 1.37232i | ||||||||
\(794\) | − | 28.2825i | − | 1.00371i | ||||||
\(795\) | 19.4820 | 0.690954 | ||||||||
\(796\) | −80.1448 | −2.84066 | ||||||||
\(797\) | −23.8003 | −0.843051 | −0.421525 | − | 0.906817i | \(-0.638505\pi\) | ||||
−0.421525 | + | 0.906817i | \(0.638505\pi\) | |||||||
\(798\) | 21.9008 | + | 4.66332i | 0.775279 | + | 0.165080i | ||||
\(799\) | 86.2406i | 3.05097i | ||||||||
\(800\) | −30.6302 | −1.08294 | ||||||||
\(801\) | −2.18580 | −0.0772314 | ||||||||
\(802\) | 56.6139i | 1.99911i | ||||||||
\(803\) | −30.3086 | −1.06957 | ||||||||
\(804\) | 40.9163 | 1.44301 | ||||||||
\(805\) | 29.1557 | + | 15.1018i | 1.02760 | + | 0.532270i | ||||
\(806\) | −32.5972 | −1.14819 | ||||||||
\(807\) | 19.5481 | 0.688126 | ||||||||
\(808\) | 65.1322i | 2.29134i | ||||||||
\(809\) | 5.76444 | 0.202667 | 0.101334 | − | 0.994853i | \(-0.467689\pi\) | ||||
0.101334 | + | 0.994853i | \(0.467689\pi\) | |||||||
\(810\) | −6.97756 | −0.245166 | ||||||||
\(811\) | 7.04906i | 0.247526i | 0.992312 | + | 0.123763i | \(0.0394963\pi\) | ||||
−0.992312 | + | 0.123763i | \(0.960504\pi\) | |||||||
\(812\) | 11.5203 | − | 54.1040i | 0.404284 | − | 1.89868i | ||||
\(813\) | 9.11521 | 0.319684 | ||||||||
\(814\) | −24.5782 | −0.861465 | ||||||||
\(815\) | −16.9448 | −0.593550 | ||||||||
\(816\) | 92.3652i | 3.23343i | ||||||||
\(817\) | 2.46597i | 0.0862735i | ||||||||
\(818\) | 38.1412i | 1.33358i | ||||||||
\(819\) | 12.1530 | + | 2.58774i | 0.424662 | + | 0.0904229i | ||||
\(820\) | − | 68.1938i | − | 2.38143i | ||||||
\(821\) | 7.82164 | 0.272977 | 0.136489 | − | 0.990642i | \(-0.456418\pi\) | ||||
0.136489 | + | 0.990642i | \(0.456418\pi\) | |||||||
\(822\) | 12.7002 | 0.442969 | ||||||||
\(823\) | −32.1995 | −1.12240 | −0.561202 | − | 0.827679i | \(-0.689661\pi\) | ||||
−0.561202 | + | 0.827679i | \(0.689661\pi\) | |||||||
\(824\) | −47.7100 | −1.66206 | ||||||||
\(825\) | −5.32454 | −0.185377 | ||||||||
\(826\) | −22.0165 | − | 4.68795i | −0.766051 | − | 0.163115i | ||||
\(827\) | 14.7733i | 0.513720i | 0.966449 | + | 0.256860i | \(0.0826878\pi\) | ||||
−0.966449 | + | 0.256860i | \(0.917312\pi\) | |||||||
\(828\) | 6.69639 | − | 24.3734i | 0.232716 | − | 0.847036i | ||||
\(829\) | − | 14.3958i | − | 0.499986i | −0.968248 | − | 0.249993i | \(-0.919572\pi\) | ||
0.968248 | − | 0.249993i | \(-0.0804284\pi\) | |||||||
\(830\) | −109.947 | −3.81631 | ||||||||
\(831\) | 21.0702i | 0.730917i | ||||||||
\(832\) | − | 104.314i | − | 3.61642i | ||||||
\(833\) | 44.6060 | + | 19.8980i | 1.54551 | + | 0.689426i | ||||
\(834\) | 6.56006 | 0.227156 | ||||||||
\(835\) | 57.0081i | 1.97285i | ||||||||
\(836\) | − | 51.9238i | − | 1.79582i | ||||||
\(837\) | −2.57414 | −0.0889753 | ||||||||
\(838\) | −56.3936 | −1.94808 | ||||||||
\(839\) | −46.8957 | −1.61902 | −0.809509 | − | 0.587108i | \(-0.800267\pi\) | ||||
−0.809509 | + | 0.587108i | \(0.800267\pi\) | |||||||
\(840\) | 59.0531 | + | 12.5741i | 2.03753 | + | 0.433849i | ||||
\(841\) | −13.2635 | −0.457362 | ||||||||
\(842\) | − | 3.82447i | − | 0.131800i | ||||||
\(843\) | 13.3224 | 0.458848 | ||||||||
\(844\) | 96.9398 | 3.33681 | ||||||||
\(845\) | −23.4348 | −0.806183 | ||||||||
\(846\) | − | 33.3266i | − | 1.14579i | ||||||
\(847\) | 0.632710 | − | 2.97146i | 0.0217402 | − | 0.102100i | ||||
\(848\) | 99.6591i | 3.42231i | ||||||||
\(849\) | − | 1.01643i | − | 0.0348837i | ||||||
\(850\) | 31.9163 | 1.09472 | ||||||||
\(851\) | −13.4299 | − | 3.68975i | −0.460371 | − | 0.126483i | ||||
\(852\) | − | 48.6864i | − | 1.66797i | ||||||
\(853\) | 4.65328i | 0.159325i | 0.996822 | + | 0.0796626i | \(0.0253843\pi\) | ||||
−0.996822 | + | 0.0796626i | \(0.974616\pi\) | |||||||
\(854\) | 12.2255 | − | 57.4158i | 0.418348 | − | 1.96473i | ||||
\(855\) | −8.12225 | −0.277775 | ||||||||
\(856\) | 26.3649i | 0.901134i | ||||||||
\(857\) | − | 0.670362i | − | 0.0228991i | −0.999934 | − | 0.0114496i | \(-0.996355\pi\) | ||
0.999934 | − | 0.0114496i | \(-0.00364459\pi\) | |||||||
\(858\) | − | 39.7469i | − | 1.35694i | ||||||
\(859\) | 42.3106i | 1.44362i | 0.692091 | + | 0.721810i | \(0.256690\pi\) | ||||
−0.692091 | + | 0.721810i | \(0.743310\pi\) | |||||||
\(860\) | 10.7154i | 0.365391i | ||||||||
\(861\) | −2.75503 | + | 12.9387i | −0.0938911 | + | 0.440950i | ||||
\(862\) | − | 67.4860i | − | 2.29858i | ||||||
\(863\) | −5.03007 | −0.171226 | −0.0856129 | − | 0.996328i | \(-0.527285\pi\) | ||||
−0.0856129 | + | 0.996328i | \(0.527285\pi\) | |||||||
\(864\) | − | 18.0561i | − | 0.614281i | ||||||
\(865\) | − | 50.8653i | − | 1.72947i | ||||||
\(866\) | −72.4567 | −2.46218 | ||||||||
\(867\) | − | 31.6864i | − | 1.07612i | ||||||
\(868\) | 35.1081 | + | 7.47555i | 1.19165 | + | 0.253737i | ||||
\(869\) | 4.72052 | 0.160133 | ||||||||
\(870\) | 27.6795i | 0.938422i | ||||||||
\(871\) | 36.4591 | 1.23537 | ||||||||
\(872\) | − | 39.3063i | − | 1.33108i | ||||||
\(873\) | 7.74499 | 0.262128 | ||||||||
\(874\) | 10.7529 | − | 39.1382i | 0.363722 | − | 1.32387i | ||||
\(875\) | −4.71048 | + | 22.1223i | −0.159243 | + | 0.747869i | ||||
\(876\) | −50.8937 | −1.71954 | ||||||||
\(877\) | −47.3377 | −1.59848 | −0.799241 | − | 0.601011i | \(-0.794765\pi\) | ||||
−0.799241 | + | 0.601011i | \(0.794765\pi\) | |||||||
\(878\) | 54.9789i | 1.85545i | ||||||||
\(879\) | 7.34305i | 0.247675i | ||||||||
\(880\) | − | 107.518i | − | 3.62443i | ||||||
\(881\) | 2.66556 | 0.0898051 | 0.0449026 | − | 0.998991i | \(-0.485702\pi\) | ||||
0.0449026 | + | 0.998991i | \(0.485702\pi\) | |||||||
\(882\) | −17.2375 | − | 7.68935i | −0.580415 | − | 0.258914i | ||||
\(883\) | 28.7945 | 0.969013 | 0.484506 | − | 0.874788i | \(-0.338999\pi\) | ||||
0.484506 | + | 0.874788i | \(0.338999\pi\) | |||||||
\(884\) | 172.712i | 5.80893i | ||||||||
\(885\) | 8.16516 | 0.274469 | ||||||||
\(886\) | 52.2526 | 1.75546 | ||||||||
\(887\) | − | 1.89674i | − | 0.0636862i | −0.999493 | − | 0.0318431i | \(-0.989862\pi\) | ||
0.999493 | − | 0.0318431i | \(-0.0101377\pi\) | |||||||
\(888\) | −25.6102 | −0.859421 | ||||||||
\(889\) | 10.5000 | − | 49.3122i | 0.352159 | − | 1.65388i | ||||
\(890\) | −15.2515 | −0.511233 | ||||||||
\(891\) | − | 3.13874i | − | 0.105152i | ||||||
\(892\) | 15.9488i | 0.534005i | ||||||||
\(893\) | − | 38.7940i | − | 1.29819i | ||||||
\(894\) | −53.0202 | −1.77326 | ||||||||
\(895\) | 24.6224 | 0.823037 | ||||||||
\(896\) | −13.1021 | + | 61.5326i | −0.437711 | + | 2.05566i | ||||
\(897\) | 5.96693 | − | 21.7183i | 0.199230 | − | 0.725154i | ||||
\(898\) | 40.3377 | 1.34609 | ||||||||
\(899\) | 10.2114i | 0.340570i | ||||||||
\(900\) | −8.94090 | −0.298030 | ||||||||
\(901\) | − | 52.5310i | − | 1.75006i | ||||||
\(902\) | 42.3164 | 1.40898 | ||||||||
\(903\) | 0.432901 | − | 2.03307i | 0.0144060 | − | 0.0676564i | ||||
\(904\) | 181.808i | 6.04685i | ||||||||
\(905\) | 27.3827 | 0.910233 | ||||||||
\(906\) | 12.7335i | 0.423043i | ||||||||
\(907\) | − | 12.9751i | − | 0.430833i | −0.976522 | − | 0.215416i | \(-0.930889\pi\) | ||
0.976522 | − | 0.215416i | \(-0.0691108\pi\) | |||||||
\(908\) | 44.9611 | 1.49209 | ||||||||
\(909\) | 7.38574i | 0.244970i | ||||||||
\(910\) | 84.7986 | + | 18.0561i | 2.81104 | + | 0.598554i | ||||
\(911\) | 26.8082i | 0.888196i | 0.895978 | + | 0.444098i | \(0.146476\pi\) | ||||
−0.895978 | + | 0.444098i | \(0.853524\pi\) | |||||||
\(912\) | − | 41.5490i | − | 1.37583i | ||||||
\(913\) | − | 49.4578i | − | 1.63682i | ||||||
\(914\) | − | 71.7124i | − | 2.37204i | ||||||
\(915\) | 21.2936i | 0.703944i | ||||||||
\(916\) | 57.1041 | 1.88677 | ||||||||
\(917\) | −26.2611 | − | 5.59176i | −0.867218 | − | 0.184656i | ||||
\(918\) | 18.8142i | 0.620963i | ||||||||
\(919\) | − | 42.9983i | − | 1.41838i | −0.705016 | − | 0.709191i | \(-0.749060\pi\) | ||
0.705016 | − | 0.709191i | \(-0.250940\pi\) | |||||||
\(920\) | 28.9940 | − | 105.532i | 0.955905 | − | 3.47929i | ||||
\(921\) | 9.98101 | 0.328886 | ||||||||
\(922\) | 64.1030i | 2.11112i | ||||||||
\(923\) | − | 43.3827i | − | 1.42796i | ||||||
\(924\) | −9.11521 | + | 42.8086i | −0.299868 | + | 1.40830i | ||||
\(925\) | 4.92648i | 0.161982i | ||||||||
\(926\) | −71.0249 | −2.33402 | ||||||||
\(927\) | −5.41013 | −0.177692 | ||||||||
\(928\) | −71.6272 | −2.35128 | ||||||||
\(929\) | − | 3.74546i | − | 0.122884i | −0.998111 | − | 0.0614422i | \(-0.980430\pi\) | ||
0.998111 | − | 0.0614422i | \(-0.0195700\pi\) | |||||||
\(930\) | −17.9612 | −0.588972 | ||||||||
\(931\) | −20.0653 | − | 8.95081i | −0.657614 | − | 0.293351i | ||||
\(932\) | −48.8607 | −1.60048 | ||||||||
\(933\) | 9.95988 | 0.326072 | ||||||||
\(934\) | −24.7572 | −0.810079 | ||||||||
\(935\) | 56.6735i | 1.85342i | ||||||||
\(936\) | − | 41.4158i | − | 1.35372i | ||||||
\(937\) | −33.4242 | −1.09192 | −0.545960 | − | 0.837811i | \(-0.683835\pi\) | ||||
−0.545960 | + | 0.837811i | \(0.683835\pi\) | |||||||
\(938\) | −54.1683 | − | 11.5340i | −1.76866 | − | 0.376599i | ||||
\(939\) | − | 19.6634i | − | 0.641690i | ||||||
\(940\) | − | 168.571i | − | 5.49819i | ||||||
\(941\) | 26.6813 | 0.869785 | 0.434892 | − | 0.900482i | \(-0.356786\pi\) | ||||
0.434892 | + | 0.900482i | \(0.356786\pi\) | |||||||
\(942\) | 25.5715i | 0.833164i | ||||||||
\(943\) | 23.1224 | + | 6.35267i | 0.752968 | + | 0.206871i | ||||
\(944\) | 41.7685i | 1.35945i | ||||||||
\(945\) | 6.69639 | + | 1.42586i | 0.217834 | + | 0.0463832i | ||||
\(946\) | −6.64924 | −0.216185 | ||||||||
\(947\) | 27.3266 | 0.887996 | 0.443998 | − | 0.896028i | \(-0.353560\pi\) | ||||
0.443998 | + | 0.896028i | \(0.353560\pi\) | |||||||
\(948\) | 7.92663 | 0.257445 | ||||||||
\(949\) | −45.3497 | −1.47211 | ||||||||
\(950\) | −14.3571 | −0.465805 | ||||||||
\(951\) | − | 26.0420i | − | 0.844470i | ||||||
\(952\) | 33.9048 | − | 159.230i | 1.09886 | − | 5.16069i | ||||
\(953\) | − | 53.2366i | − | 1.72450i | −0.506480 | − | 0.862252i | \(-0.669054\pi\) | ||
0.506480 | − | 0.862252i | \(-0.330946\pi\) | |||||||
\(954\) | 20.3000i | 0.657236i | ||||||||
\(955\) | − | 31.0160i | − | 1.00365i | ||||||
\(956\) | −62.6021 | −2.02470 | ||||||||
\(957\) | −12.4512 | −0.402489 | ||||||||
\(958\) | −7.36904 | −0.238083 | ||||||||
\(959\) | −12.1884 | − | 2.59527i | −0.393584 | − | 0.0838056i | ||||
\(960\) | − | 57.4774i | − | 1.85507i | ||||||
\(961\) | 24.3738 | 0.786252 | ||||||||
\(962\) | −36.7755 | −1.18569 | ||||||||
\(963\) | 2.98968i | 0.0963411i | ||||||||
\(964\) | −97.4733 | −3.13940 | ||||||||
\(965\) | 7.67763 | 0.247152 | ||||||||
\(966\) | −15.7359 | + | 30.3799i | −0.506295 | + | 0.977456i | ||||
\(967\) | −18.9639 | −0.609839 | −0.304919 | − | 0.952378i | \(-0.598630\pi\) | ||||
−0.304919 | + | 0.952378i | \(0.598630\pi\) | |||||||
\(968\) | −10.1263 | −0.325471 | ||||||||
\(969\) | 21.9008i | 0.703554i | ||||||||
\(970\) | 54.0412 | 1.73516 | ||||||||
\(971\) | −40.9527 | −1.31424 | −0.657118 | − | 0.753788i | \(-0.728225\pi\) | ||||
−0.657118 | + | 0.753788i | \(0.728225\pi\) | |||||||
\(972\) | − | 5.27053i | − | 0.169052i | ||||||
\(973\) | −6.29571 | − | 1.34054i | −0.201831 | − | 0.0429758i | ||||
\(974\) | −57.6322 | −1.84665 | ||||||||
\(975\) | −7.96693 | −0.255146 | ||||||||
\(976\) | −108.926 | −3.48664 | ||||||||
\(977\) | 3.69363i | 0.118170i | 0.998253 | + | 0.0590849i | \(0.0188183\pi\) | ||||
−0.998253 | + | 0.0590849i | \(0.981182\pi\) | |||||||
\(978\) | − | 17.6563i | − | 0.564585i | ||||||
\(979\) | − | 6.86066i | − | 0.219268i | ||||||
\(980\) | −87.1897 | − | 38.8939i | −2.78517 | − | 1.24242i | ||||
\(981\) | − | 4.45718i | − | 0.142307i | ||||||
\(982\) | 58.7235 | 1.87394 | ||||||||
\(983\) | −42.0674 | −1.34174 | −0.670872 | − | 0.741574i | \(-0.734080\pi\) | ||||
−0.670872 | + | 0.741574i | \(0.734080\pi\) | |||||||
\(984\) | 44.0932 | 1.40564 | ||||||||
\(985\) | 43.8022 | 1.39565 | ||||||||
\(986\) | 74.6347 | 2.37685 | ||||||||
\(987\) | −6.81027 | + | 31.9837i | −0.216773 | + | 1.01805i | ||||
\(988\) | − | 77.6918i | − | 2.47170i | ||||||
\(989\) | −3.63325 | − | 0.998203i | −0.115530 | − | 0.0317410i | ||||
\(990\) | − | 21.9008i | − | 0.696052i | ||||||
\(991\) | 39.5972 | 1.25785 | 0.628923 | − | 0.777468i | \(-0.283496\pi\) | ||||
0.628923 | + | 0.777468i | \(0.283496\pi\) | |||||||
\(992\) | − | 46.4790i | − | 1.47571i | ||||||
\(993\) | 8.65628i | 0.274699i | ||||||||
\(994\) | −13.7244 | + | 64.4549i | −0.435310 | + | 2.04439i | ||||
\(995\) | −39.3497 | −1.24747 | ||||||||
\(996\) | − | 83.0489i | − | 2.63150i | ||||||
\(997\) | − | 13.1814i | − | 0.417458i | −0.977974 | − | 0.208729i | \(-0.933067\pi\) | ||
0.977974 | − | 0.208729i | \(-0.0669326\pi\) | |||||||
\(998\) | 48.8647 | 1.54679 | ||||||||
\(999\) | −2.90409 | −0.0918815 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 483.2.h.c.160.2 | yes | 12 | |
3.2 | odd | 2 | 1449.2.h.e.1126.9 | 12 | |||
7.6 | odd | 2 | inner | 483.2.h.c.160.3 | yes | 12 | |
21.20 | even | 2 | 1449.2.h.e.1126.11 | 12 | |||
23.22 | odd | 2 | inner | 483.2.h.c.160.1 | ✓ | 12 | |
69.68 | even | 2 | 1449.2.h.e.1126.12 | 12 | |||
161.160 | even | 2 | inner | 483.2.h.c.160.4 | yes | 12 | |
483.482 | odd | 2 | 1449.2.h.e.1126.10 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
483.2.h.c.160.1 | ✓ | 12 | 23.22 | odd | 2 | inner | |
483.2.h.c.160.2 | yes | 12 | 1.1 | even | 1 | trivial | |
483.2.h.c.160.3 | yes | 12 | 7.6 | odd | 2 | inner | |
483.2.h.c.160.4 | yes | 12 | 161.160 | even | 2 | inner | |
1449.2.h.e.1126.9 | 12 | 3.2 | odd | 2 | |||
1449.2.h.e.1126.10 | 12 | 483.482 | odd | 2 | |||
1449.2.h.e.1126.11 | 12 | 21.20 | even | 2 | |||
1449.2.h.e.1126.12 | 12 | 69.68 | even | 2 |